Long-term planning of an underground mine using mixed-integer linear programming
CIM Bulletin, Vol. 98, No. 1089, 2005
The preparation of a long-term plan requires an understanding of all the facets of a mine, among them, the access and other infrastructures; the general layout; the geology, reserves, and extraction plan of every sector; and the productivity of the workers. The planner combines all these elements, often in an intuitive way, into a number of alternative plans, trying to identify the most likely outcomes and problems. The final plan that is compiled is functional, but there is no certainty that it is optimal.Though operation research has been used for many years in open-pits, there has been a limited use of linear programming for long-term planning in underground mines. Commercially available software can determine the most time-efficient development and production plan based on sets of precedents and development rates, identifying the critical path and producing a graphical output. This plan, however, is not taking into consideration issues such as blending or cash flow optimization. It is recognized by many authors that mixed-integer programming is required to incorporate sequencing, blending, and economical considerations. Programs have been written to solve problems specific to mines or regional operations.Mixed-integer linear programming is used to prepare the long-term development and production plan of an underground mine. The objective is to maximize the cash flow through selecting the sectors to be mined and determining the sequence of development and production that can reduce the fixed costs of operations, while meeting the mill feed requirements. Two sets of constraints are taken into consideration. The first set is related to each individual zone and the constraints define the maximum rates of development and production that can be achieved. The second set deals with the overall plan, looking at meeting minimum requirements in terms of tonnes and grades sent to the mill, maximum development capacity for mining operations, and the quality of the reserves mined.The deposit is a narrow vein with extensive dimensions along strike and depth. Many economical sectors are identified within it, each with their own specific characteristics. As such, each zone can be defined by its reserves (tonnes, grades, value per tonne, and quality), required development (pre-production and production metres, and percentage of production development in ore), and the mining method with its direct cost. The mine is in operation, with some sectors already in production, others in development, and the rest are still undeveloped. Apart from the costs of development and production, the milling variable and the mine fixed costs are added.A critical examination of the results can be done by changing the objective function and eliminating some constraints, and comparing the new solutions to the original. For example, a blue-sky plan can be developed by not constraining development rates or by changing the objective function to minimize the development time. The new solutions can be analyzed to determine if the development rates obtained are technically feasible. The definition drilling program can be refined by removing the constraint on mining the best quality ore first to determine if there are any advantages in accelerating the work in a particular sector of the mine. The impact of leaving mine sectors out of the plan can also be studied. In general, management can use this approach to study various “what if” scenarios and determine a proper course of action.